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Nonnegative matrix factorization (NMF) is a standard linear dimensionality reduction technique for nonnegative data sets. In order to measure the discrepancy between the input data and the low-rank approximation, the Kullback-Leibler (KL)…
Referring back to the original text in the course of hierarchical learning is a common human trait that ensures the right direction of learning. The models developed based on the concept of Non-negative Matrix Factorization (NMF), in this…
Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…
Low dimensional nonlinear structure abounds in datasets across computer vision and machine learning. Kernelized matrix factorization techniques have recently been proposed to learn these nonlinear structures for denoising, classification,…
Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…
In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the…
Linear dimensionality reduction techniques are powerful tools for image analysis as they allow the identification of important features in a data set. In particular, nonnegative matrix factorization (NMF) has become very popular as it is…
Nonnegative matrix factorization (NMF) seeks a low-rank approximation $X \approx UV^T$ with nonnegative factors and is commonly solved using interior methods that enforce feasibility throughout optimization. We show that such…
In this paper we consider the Nonnegative Matrix Factorization (NMF) problem: given an (elementwise) nonnegative matrix $V \in \R_+^{m\times n}$ find, for assigned $k$, nonnegative matrices $W\in\R_+^{m\times k}$ and $H\in\R_+^{k\times n}$…
A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a…
We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower…
Nonnegative matrix factorization (NMF) is a relatively new unsupervised learning algorithm that decomposes a nonnegative data matrix into a parts-based, lower dimensional, linear representation of the data. NMF has applications in image…
In this paper we consider the Nonnegative Matrix Factorization (NMF) problem: given an (elementwise) nonnegative matrix $V \in \R_+^{m\times n}$ find, for assigned $k$, nonnegative matrices $W\in\R_+^{m\times k}$ and $H\in\R_+^{k\times n}$…
The Nonnegative Matrix Factorization (NMF) of the rating matrix has shown to be an effective method to tackle the recommendation problem. In this paper we propose new methods based on the NMF of the rating matrix and we compare them with…
In this work, we focus on connections between $K$-means clustering approaches and Orthogonal Nonnegative Matrix Factorization (ONMF) methods. We present a novel framework to extract the distance measure and the centroids of the $K$-means…
Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases and other information retrieval and clustering applications. In this report, we define an exact version of NMF. Then…
Non-negative matrix factorization (NMF) is a fundamental non-convex optimization problem with numerous applications in Machine Learning (music analysis, document clustering, speech-source separation etc). Despite having received extensive…
Recently, many works have demonstrated that Symmetric Non-negative Matrix Factorization~(SymNMF) enjoys a great superiority for various clustering tasks. Although the state-of-the-art algorithms for SymNMF perform well on synthetic data,…
Learning multi-view data is an emerging problem in machine learning research, and nonnegative matrix factorization (NMF) is a popular dimensionality-reduction method for integrating information from multiple views. These views often provide…
Non-negative Matrix Factorisation (NMF) has been extensively used in machine learning and data analytics applications. Most existing variations of NMF only consider how each row/column vector of factorised matrices should be shaped, and…